Geant4 Simulations for the Radon Electric Dipole Moment Search at

(σ + ) along the axis of the B field, the transition must satisfy the selection rule
∆m F = +1. Because there is no m F = +4 magnetic substate in the 2 P 1/2 excited
state, see Figure 2.4, any electrons in the m F = +3 magnetic substate of the 2 S 1/2
ground state will remain trapped there. As the 2 P 1/2 excited states relax through
photon emission the probability of populating the m F = +3 magnetic substate of
the 2 S 1/2 ground state is determined by the selection rule ∆m = ±1 or 0 for photon
emission. After several S 1/2 - P 1/2 - S 1/2 pumping cycles almost all the atoms will
end up trapped in the m F = +3 magnetic substate of the 2 S 1/2 level, and thus, the
m F = +3 ground state has been optically “pumped” into an ensemble of atoms with
a very high degree of polarization.
2.3.2 Spin Exchange
Opticallypumpedalkali-metalatomscanpolarizenoble-gasatomsviaspin-exchange
interactions. TheHamiltonianthatdescribes theinteractionbetween alkali-metaland
noble-gas atoms is [29]
H = AI·S+γN·S+αK·S+g s µ B B·S+g I µ B B·I+g K µ B B·K+··· , (2.15)
where S is the spin of the alkai-metal valence electron, I is the alkai-metal nuclear
spin, K is the noble-gas nuclear spin, N is the rotational angular momentum of the
formed alkai-metal noble-gas van der Waals molecule, and B is the external magnetic
field.
The transfer of angular momentum can occur while the atoms are bound in shortlived
van der Waals molecules or by simple binary collisions between atoms, shown
in Figure 2.5. For light noble gases, such as 3 He, binary collisions dominate the
transfer of angular momentum and the contribution from van der Waals molecules is
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